A method for performing quantum calculation, in which multiple quantum bits are formed by using a semiconductor quantum dot structure having a plurality of aligned semiconductor quantum dots, has conventionally been proposed. As the method for forming multiple quantum bits by using semiconductor quantum dots, a method that uses electron spin has been proposed. Electron spin under a strong magnetic field behaves basically as a two-level system, so that an electron spin-up state and an electron spin-down state are related to a one bit state. A method that uses electron spin resonance (ESR) to manipulate bits has also been proposed. For example, it has been proposed to carry out quantum calculation by irradiating quantum dots with a high-frequency magnetic field under a strong magnetic field, determining an electron spin state by ESR control, and then changing an interaction between the quantum dots (see Non-Patent Documents 1, 2, and 3 below).
As a method for controlling ESR of electron spin in semiconductor quantum dots, a method for applying microwaves to a micro coil formed above quantum dots (see Non-Patent Document 3), and a method for directly applying microwaves to a control electrode (see Non-Patent Documents 4 and 5) have been proposed.
A conventional method for controlling ESR of electron spin in semiconductor quantum dots will be described below in accordance with Non-Patent Document 3.
FIG. 1 shows a top view of a conventional electronic device using quantum dots. FIG. 2 shows a schematic side view of the electronic device.
As shown in FIGS. 1 and 2, when an aluminum gallium arsenide crystal layer (AlGaAs) 12 is epitaxially grown on a gallium arsenide (GaAs) crystal substrate 11, a two-dimensional electron gas layer (2DEG layer) 13 with a thickness of about 10 nm is formed at the heterojunction interface between these two crystals. This 2DEG layer 13 is located approximately 100 nm below the surface of the AlGaAs crystal layer 12 which is an epitaxial layer of AlGaAs. Gate electrodes 2, 3, 4, and 5, i.e. a quantum dot coupling control electrode 2, a right electrode for forming a quantum dot 3, a left electrode for forming a quantum dot 4, a center gate electrode 5, are formed on the AlGaAs crystal layer 12. When a negative voltage is applied to the gate electrodes 2, 3, 4, and 5, a depletion layer extends from just beneath them. Each depletion layer extends to the 2DEG layer 13, and as the magnitude of the negative voltage applied to the gate electrodes 2, 3, 4, and 5 is increased, the 2DEG layer 13 loses electron carriers from the parts reached by the depletion layer. When the negative applied voltage is further increased, electron carriers remain only in an island-shaped (almost disc-shaped) portions in the 2DEG layer 13, which are a quantum dot 8 and a quantum dot 9. Then, a calixarene insulating film 14 is deposited on the upper surface of a semiconductor crystal substrate 1. A pattern of a high-frequency micro coil 34 is formed on the calixarene insulating film 14, by the electron beam vacuum evaporation method, so as to be 90 nm away from the surfaces of the gate electrodes 2, 3, 4, and 5. Adjusting the voltages applied to the gate electrodes 2, 3, 4, and 5 allows both quantum dots 8 and 9 to have only a single electron. Then, an external magnetic field 17 is applied to fix the energy state of electron spin.
In order to form a quantum bit by using this conventional electronic device, electron spin information of all quantum dots is initialized, and then the information is written into a first quantum dot by using ESR control (N). A high-frequency magnetic field is induced by applying a high-frequency current to the high-frequency micro coil 34 shown in FIGS. 1 and 2, then electron spin in the quantum dot 8 is manipulated by the ESR control. The ESR control will be described with reference to energy diagrams shown in FIG. 3. FIG. 3(a) to FIG. 3(c) show time-dependent changes of electron spin states during the ESR control. 35 shows an energy state of a drain electrode and 36 shows an energy state of a source electrode. The shaded portion is filled with electrons, so that electrons in the energy states below the uppermost plane do not flow. 37 shows a tunneling barrier, 38 shows a spin-up electron spin in the ground state, and 39 shows a spin-down electron spin in the excited state.
Electrons are first injected into the quantum dot 8 on the left side by electrode operation. After sufficiently long time (1 millisecond to 1 second), electron spins in both quantum dots 8 and 9 are aligned, and no current flows according to the Pauli principle (see Non-Patent Document 6). That is, in FIG. 3 (a), 40 indicates that no current is flowing between the quantum dots 8 and 9, showing that the electron spin information is initialized. Then a high-frequency magnetic field is applied to perform the ESR control. As shown in FIG. 3 (b), the ESR control reverses the electron spin 39. If a tunneling probability between the quantum dots is high enough, the fact that the ESR control has been performed can be observed as a current flow 16 between the quantum dots, as shown in FIG. 3 (c). In this way, it is confirmed that electron spin states are changed by the ESR control.
To fabricate multiple quantum bits by using the conventional electronic device, it is necessary to precisely control a coupling state of electron spin between quantum dots and to rapidly control the electron spin in the quantum dot (B). FIG. 4 shows a method for controlling a coupling state between electron spin in accordance with Non-Patent Document 2. This device is nearly the same as that shown in FIGS. 1 and 2, so that it will be described in reference with these figures. As shown in FIG. 4 (a), two electron spins 38 and 39 are assumed to be oppositely directed in the initial state. Differing from the description (A) given above, it is assumed that the energy states of the electron spins 38 and 39 are lower than the energy states 35 and 36 of the drain electrode and the source electrode, respectively, and that no current is flowing. An interaction 20 between the electron spins can be enhanced by increasing a voltage applied to the left gate electrode 4 for forming a quantum dot by a small amount without causing electric charge transfer, or by relatively decreasing the influence of the depletion layer under the center gate electrode 5, before the electron spins 38 and 39 are aligned due to electron spin relaxation and electron spin block occurs, as shown in FIG. 4 (b). Then, the electron spins interact with each other and become in the aligned state, as shown in FIG. 4 (c). In this way, the electrons interact with each other and alternate between a spin aligned state and a spin opposed state. The direction of the electron spin can always be reversed by keeping the interaction time constant. This operation indicates a logical NOT operation. It may seemingly easy to realize a quantum bit and perform quantum calculation by combining (A) and (B) described above.
Non-Patent Document 1: Loss, D. & DiVincenzo D. P., Quantum computation with quantum dots. Phys. Rev. A57, pp. 120-126 (1998).
Non Patent Document 2: Petta, J. R. et al., Coherent manipulation of coupled electron spins in semiconductor quantum dots, Science 309, pp. 2180-2184 (2005).
Non-Patent Document 3: Koppens, F. H. L. et al., Driven coherent oscillations of a single electron spin in a quantum dot, Nature 442, pp. 766 (2006).
Non-Patent Document 4: Nowack, K. C. et al., Coherent Control of a Single Electron Spin with Electric Fields, Science Published Online Nov. 1 (2007)
Non-Patent Document 5: Laird E. A. et al., http://arxiv.org/abs/0707.0557 (2007)
Non-Patent Document 6: Ono, K. et al., Current rectification by Pauli exclusion in a weakly coupled double quantum dot system, Science 297, pp. 1313-1317 (2002)
Non-Patent Document 7: Tarucha et al., Phys. Rev. Lett. 77, pp. 3613 (1996).
Disclosure Of Invention
However, in order to form multiple quantum bits comprising a plurality of quantum dots, it is necessary to perform ESR control rapidly, precisely and individually on electron spin in each quantum dot.
In the conventional ESR control methods, however, rapid electron spin in all quantum dots are controlled only in uniform and simultaneous way, having difficulties in realizing multiple bits.
In view of the situation described above, an object of the present invention is to provide an electronic device using quantum dots, which comprises a ferromagnetic magnet, and can carry out quantum calculation by performing ESR control on each multiple quantum bit individually in a power saving way.
To fulfill the above object, the present invention provides:
[1] An electronic device using quantum dots, comprising a ferromagnetic magnet disposed in the vicinity of each quantum dot of a plurality of aligned semiconductor quantum dots and transforming a high frequency electric field into a high frequency magnetic field, wherein the ferromagnetic magnet is a ferromagnetic thin film that is disposed on the quantum dots with a dielectric material therebetween.
[2] The electronic device of [1], wherein a frequency of the high frequency electric field is 1.6 GHz and more and 300 GHz or less.
[3] The electronic device of [2], wherein a frequency of the high frequency electric field is 1.6 GHz and more and 3 GHz or less.
[4] The electronic device of [2], wherein a frequency of the high frequency electric field is 3 GHz and more and 30 GHz or less.
[5] The electronic device of [2], wherein a frequency of the high frequency electric field is 30 GHz and more and 300 GHz or less.
[6] The electronic device of [1], wherein the ferromagnetic thin film is made from cobalt or cobalt alloy containing 50% and more of cobalt.
[7] The electronic device of [6], wherein a thickness of the ferromagnetic thin film is from 0.05 μm to 1 μm, a width of the ferromagnetic thin film is from 0.3 μm to 0.4 μm, and a length of the ferromagnetic thin film is 1 μm.
[8] The electronic device of [1], wherein the ferromagnetic thin film is made from nickel or nickel alloy containing 50% and more of nickel.
[9] The electronic device of [8], wherein a thickness of the ferromagnetic thin film is from 0.15 μm to 3 μm, a width of the ferromagnetic thin film is from 0.3 μm to 0.4 μm, and a length of the ferromagnetic thin film is 1 μm.
[10] The electronic device of [1], wherein the ferromagnetic thin film is made from dysprosium or dysprosium alloy containing 50% and more of dysprosium.
[11] The electronic device of [10], wherein a thickness of the ferromagnetic thin film is from 0.025 μm to 1 μm, a width of the ferromagnetic thin film is from 0.3 μm to 0.4 μm, and a length of the ferromagnetic thin film is 1 μm.
[12] The electronic device of [1], wherein the ferromagnetic thin film is made from iron or iron alloy containing 50% and more of iron.
[13] The electronic device of [12], wherein a thickness of the ferromagnetic thin film is from 0.025 μm to 1 μm, a width of the ferromagnetic thin film is from 0.3 μm to 0.4 μm, and a length of the ferromagnetic thin film is 1 μm.
[14] The electronic device of [1], wherein the ferromagnetic thin film is made from chromium or chromium alloy containing 50% and more of chromium.
[15] The electronic device of [14], wherein a thickness of the ferromagnetic thin film is from 0.025 μm to 1 μm, a width of the ferromagnetic thin film is from 0.3 μm to 0.4 μm, and a length of the ferromagnetic thin film is 1 μm.
[16] The electronic device of [1], wherein a gradient magnetic field and a parallel magnetic field with respect to the surface of the quantum dots are generated due to a magnetic field generated by the ferromagnetic thin film.
[17] The electronic device of [1], wherein an energy state of electron spin in each quantum dot is changed by applying a strong external magnetic field under an ultra-low temperature, and each quantum dot has an individual energy state by the action of the parallel magnetic field.
[18] The electronic device of [16], wherein an electron disposed in the vicinity of the quantum dots are electrically driven under the influence of the gradient magnetic field, and electron spin resonance is realized.
[19] The electronic device of [18], wherein an electron spin state can be manipulated to be a spin-up state and a spin-down state by the electron spin resonance, and the electron spin state is related to a bit, thereby setting a quantum bit
[20] The electronic device of [1], wherein each quantum dot has a different energy state by the action of the ferromagnetic magnet.
[21] The electronic device of [1], wherein electron spin can be manipulated independently by applying a high frequency electric field with different frequency to each quantum dot, according to the electron spin resonance principle.
[22] The electronic device of [1], wherein electrons present in the quantum dots mutually form an electronic coupling state.
[23] The electronic device of [1], further comprising a control electrode disposed halfway between the quantum dots, wherein a coupling state of electrons is controlled by applying a voltage to the control electrode to extend or contract a depletion layer under the control electrode.
[24] The electronic device of [23], wherein quantum calculation is performed by manipulating the coupling state of electrons.
[25] The electronic device of [1], wherein each quantum dot has a horizontal quantum dot structure with a gate electrode for forming a quantum dot, the gate electrode being disposed on a surface of a semiconductor crystal substrate, the substrate having a two-dimensional electron gas layer at a heterojunction interface between a gallium arsenide and an aluminum gallium arsenide.
[26] The electronic device of [1], wherein each quantum dot has a horizontal quantum dot structure with a gate electrode for forming a quantum dot, the gate electrode being disposed on a surface of a semiconductor crystal substrate, the substrate having a two-dimensional electron gas layer at a heterojunction interface between a silicon and a silicon germanium.
[27] The electronic device of [25] or [26], wherein each quantum dot has a vertical quantum dot structure in which the two-dimensional electron gas layer is geometrically cut out and a metallic electrode is disposed on the periphery of the cut out layer.
[28] The electronic device of [1], wherein the ferromagnetic magnet is made from a ferromagnetic metal, an oxide ferromagnetic metal, a superconductive metal, or an oxide superconductive metal.
[29] The electronic device of [1], wherein a distance from the ferromagnetic magnet to each semiconductor quantum dot is different.
[30] The electronic device of [29], wherein the distance from the ferromagnetic magnet to each semiconductor quantum dot varies from 0.15 μm to 0.5 μm, and a thickness of the ferromagnetic magnet is 0.1 μm.
[31] The electronic device of [1], wherein a thickness of the ferromagnetic magnet in the nearest neighborhood of each quantum dots is varied.
[32] The electronic device of [31], wherein a thickness of the ferromagnetic magnet varies from 0.025 μm to 1 μm.
[33] The electronic device of [23], [25], or [26], wherein a dielectric film is disposed between the ferromagnetic magnet and the electrodes or the gate electrodes for forming a quantum dot.
[34] The electronic device of [33], wherein the dielectric film is an electron beam lithography resist, a photoresist or silicon dioxide, or silicon nitride.
[35] The electronic device of [23], wherein the dimensions of the ferromagnetic magnet, the control electrode, and the gate electrodes for forming a quantum dot are changed uniformly so as to provide the same function only by changing a magnitude of applied voltage.
[36] The electronic device of [1], further comprising a control electrode, an electrode for forming a quantum dot, and a readout quantum point contact gate electrode in the vicinity of the semiconductor quantum dots, and further comprising a quantum point contact exhibiting one dimensional quantized electron conduction phenomenon.
[37] The electronic device of [1], further comprising a quantum point contact which changes its conductivity depending on the number of electric charges in the neighboring quantum dots.
[38] The electronic device of [1], wherein readout of an electron spin state is performed by means of detection of an electron coupling state between the quantum dots and an electric charge.
[39] The electronic device of [1], wherein an electron spin polarized current utilizing electron spin alignment due to a leakage magnetic field can be injected in the vicinity of the ferromagnetic thin film.
[40] The electronic device of [1], wherein a flip-flop operation can be performed by controlling an electron spin state of each quantum dot uniquely.
[41] The electronic device of [17], wherein quantum calculation can be performed by controlling a coupling state between the electron spins.
In other words, the present invention provides:
[A] A electric device using quantum dots, comprising a structure in which a dielectric film such as an electron beam resist is deposited on top surfaces of gate electrodes forming a plurality of quantum dots, and a ferromagnetic magnet is disposed on the dielectric film. A component, which is perpendicular to a surface of a two-dimensional electron gas layer (2DEG), of a local magnetic field produced by the ferromagnetic magnet, generates a gradient magnetic field. When a high-frequency electric field is applied to electrons in the gradient magnetic field, the electrons are electrically oscillated, and the oscillations produce a high-frequency magnetic field that is necessary for performing ESR control. The present invention achieves the same effect as the micro coil method of Non-Patent Document 3 in which a magnetic field is induced by current, in at least 10 times more power saving way.
[B] The electronic device of [A], wherein a magnetic field component, which is generated by the ferromagnetic magnet and parallel to the 2DEG plane, changes the local magnetic field intensity to which an electron spin is subject. The magnetic field component has a magnitude of approximately 1 to 10% of an externally applied strong magnetic field. The magnetic field component changes electron spin energy by approximately 1 to 10% The changes in the local magnetic field intensity and the modulation of the electron spin energy can be controlled by changing a layout and a structure of the ferromagnetic magnet. Since the electron spin energy corresponds to a frequency of the high-frequency electric field described in [A], changing the frequency of the high-frequency electric field allows selective manipulation of the electron spin.
[C] The electronic device of [A], wherein an electron in each quantum dot mutually forms an electronic coupling state. In the electronic coupling state between electrons, an exchange interaction between electron spins (a coupling state between electron spins) can be controlled freely, by applying a voltage to an electrode disposed between the quantum dots, and by utilizing extension or contraction of a depletion layer under the electrode. Changing the coupling state allows quantum calculation.
[D] The electronic device of [A], comprising a horizontal quantum dot structure, or a vertical quantum dot structure. The horizontal quantum dot structure utilizes a two-dimensional electron gas (2DEG) generated at a heterojunction interface such as a double heterojunction interface between a gallium arsenide and an aluminum gallium arsenide, and a double heterojunction interface between a silicon and a silicon germanium. In the vertical quantum dot structure, a double heterojunction interface is geometrically cut out, and an electrode is disposed therearound.
[E] The electronic device of [A], [B], [C], and [D], wherein a similar effect is achieved when a ferromagnetic metal (Co, Ni, Fe, Cr, Py, Dy, Cd), an alloy of these metals, or an oxide ferromagnetic metal [TiO2, SrO, MnO2, LaO, (La, Sr)O] is used as the ferromagnetic magnet. When a perfect diamagnetic material such as a superconductor (Nb, NbTi, NbN) and an oxide superconductor (SrCuO) is used, a magnetic field direction is reversed, but a similar effect is also expected to be achieved.
[F] The electronic device of [A], [B], [C], and [D], wherein a similar effect is expected to be achieved when a thickness and/or a layout of the ferromagnetic magnet are changed.
[G] The electronic device of [A], [B] [C], and [D], wherein a similar effect is expected to achieved when the dielectric film is disposed between the ferromagnetic magnet and the control electrode/the gate electrodes for forming quantum dots, as long as the thickness of the dielectric film is thin enough. The dielectric film can be selected widely from an electron beam lithography resist, a photolithography resist and the like.
[H] The electronic device of [A], [B], [C], and [D], wherein when a quantum dot is scalable, the dimension of the ferromagnetic magnet and the thickness of the dielectric film are controllable, so the device becomes scalable as a whole.
[I] The electronic device of [A], [B], [C], and [D], further comprising a quantum point contact disposed in the vicinity of the quantum dots, the a quantum point contact having a feature of exhibiting a one-dimensional quantized transmission phenomenon, wherein the quantum point contact changes its conductivity by sensing changes in the number of electrons in the quantum dots, so that small changes in a electron state can be measured, and wherein, in combination with the ferromagnetic magnet, electron spin in a polarized state can be injected into the quantum dot, as the Stern-Gerlach experiment.